Subsea Boosting Day 2 November 2014 Jørgen Wessel thermodynamic design and test evaluation of centrifugal compressors is frequently based upon a polytropic analysis employing perfect-gas

Subsea Boosting Day 2

November 2014 Jørgen Wessel

November 2013 UiO MEK4450

2

Compressor Modeling

L

The Polytropic Analysis of Centrifugal Compressors

John M. Schultz, Trans. Of the ASME, ASME J. of Engineering for Power, Jan 1962 pp 69-82

The real-gas equations of polytropic analysis are derived in terms of compressibility functions X and Y which supplement the familiar compressibility factor, Z. A polytropic head factor, f, is introduced to adjust test results for deviations from perfect-gas behavior. Functions X and Y are generalized and plotted for gases in corresponding states.

The thermodynamic design and test evaluation of centrifugal compressors is frequently based upon a polytropic analysis employing perfect-gas relations. In many instances real-gas relations would be more accurate, but these are virtually unknown. The purpose of this paper is to derive the real-gas equations of polytropic analysis and to show their application to centrifugal compressor testing and design.


3

Back to Classical Thermodynamics

𝐻 −𝐻𝑜 = 𝐶𝑝∗𝑑𝑇 +

𝑇

𝑇0

𝑇𝜕𝑉

𝜕𝑇𝑃

− 𝑉 𝑑𝑃𝑃

0

𝑆 − 𝑆𝑜 = 𝐶𝑝∗

𝑇𝑑𝑇 +

𝑇

𝑇0

𝜕𝑉

𝜕𝑇𝑃

𝑑𝑃𝑃

0

Where C*p is the ideal gas state heat capacity

Question: Compressible fluid?

s

h

Entropy

En

tha

lpy

dh dhi

P+dp

p


5

The problem in 1962

• Schultz needed a convenient model for the fluid

• Little General Access to Process Simulation Tools • Limitations in Equations of State Methods

• BWR 1940, complex solution • RK 1949, limited application to mixtures • NGA 1958, Equilibrium Ratio Data for Computers

Needed an alternative which could be handled using a slide rule • I.e.: Simple log-log relationships • Utilize Corresponding States Models


6

Compressor Modeling

Classic Compressor Algorithm: Polytropic

• 𝑃𝑉𝑛 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

•𝑃𝑚

𝑇= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

•𝑃𝑛−1𝑛−𝑚

𝑍= 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Solving Bernoulli’s equation

*

1

212

1

2

1

2* lnlnpC

R

pP

PTT

P

PR

T

TC

2

1

2

1

2

1

2

1

**0

V

V

T

T

V

V

T

T

dVV

RTdTCPdVdTCWHQ

pp

1)(

*

1

21

*

12

*pC

R

ppP

PTCTTCW

11

1

1

211

P

PVPW

RTPVwhileRCCandC

Cvp

v

p **

*

*

0)()(2

1 22 wf

P

P

oiio hhdP

hhguuo

i

Bernoulli

1st Law

2nd Law 2

1

*

0

T

T

dTT

CS

p

UiO MEK4450 7

November 2013


8

Schultz shortcut: Linearization

𝑘 =𝐶𝑝

𝐶𝑣

hp= polytropic efficiency

h𝑝= 𝑉

𝑑𝑃

𝑑𝐻=

𝑉

𝜕𝐻𝜕𝑃 𝑇

+ 𝐶𝑝𝑑𝑇𝑑𝑃

𝑋 =𝑇

𝑉

𝑑𝑉

𝑑𝑇 𝑃 Z-Factor Charts

𝑌 = −𝑃

𝑉

𝑑𝑉

𝑑𝑃 𝑇


9

Hi,Si,Vi,CPi,Cvi

V/F,X,Y,n,m,

Top

Feed at P,T

Flash at Pi,Ti

Calculate To,Po,Vo

Flash at Po,To

Ho,So,To,W

Outputs Inputs • Efficiency • Composition

Schultz Algorithm: Wheel by Wheel

Not Rigorous for Multiphase

Dry Gas Compressors


10

Compressor Sizing using software

30oC 1 bar ?oC

6 bar

Find Power requirement

Feed rate 1000kg/hr

50oC

21 bar 5 oC 21 bar

U- value For 10” piping 10 km long Seawater at 4oC

75% Adiabatic Efficiency 77.9% Polytropic Efficiency

UiO MEK4450 11

November 2013

Reservoir Fluids

0

20

40

60

80

100

120

140

160

-200 -100 0 100 200 300 400 500

Temperature, oC

Pre

ssu

re, b

ar

Gas Cap

Oil

20vol% Gas

40vol% Gas

60vol% Gas

80vol% Gas

Bubble Point

Bubble Point

Dew Point

Dew Point

99.99vol% Gas

99.9vol% Gas

99vol% Gas

UiO MEK4450 12

November 2013

Basic Evolution

•the molecules have no volume themselves •there are no forces between the molecules

V

RTP

Ideal gas

van der Waals 2v

a

bv

RTP

• The molecules have a volume, which we call b. The free volume for motion is then v-b • There are forces between the molecules which must be proportional to 1/v2

UiO MEK4450

13

November 2013

Corrections to fit vapour pressure

Fits liquids better, but at a cost

SRK PR

) ( b v v

a

b v

RT P

) ( ) ( b v b b v v

a

b v

RT P

c

c

P

RT b 08664 . 0

c

c

P

RT b 0778 . 0

a P

T R a c

2 2

42748 . 0 a P

T R a c

2 2

45724 . 0

( ) [ ] 2

1 1 r T m a ( ) [ ] 2

1 1 r T m a 2

17600 . 0 57400 . 1 48000 . 0 w w a Soave 2

26952 . 0 54226 . 1 3746 . 0 w w a 2

15613 . 0 55171 . 1 48508 . 0 w w a Riazi

UiO MEK4450 14

November 2013

Issues around EOS use

Be consistent with the operator: use theirs Equilibrium Gas Phase Envelope

0.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

-100.00 -50.00 0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00 400.00

Temperature, C

Pre

ssu

re,

bar

Operating Window

Peng-Robinson SRK

Fluid Behaviour based on SRK fit to Reservoir Data

UiO MEK4450 15

November 2013

EOS Comparison: PR-AGA-8

0.6500

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

0.0000 50.0000 100.0000 150.0000 200.0000 250.0000

Pressure, bar

Z F

acto

r

PR @5C

PR @10C

PR @15C

AGA-8 @5C

AGA-8 @10C

AGA-8 @15C

UiO MEK4450 16

November 2013

EOS Comparison: SRK-AGA-8

0.6500

0.7000

0.7500

0.8000

0.8500

0.9000

0.9500

1.0000

0.0000 50.0000 100.0000 150.0000 200.0000 250.0000

Pressure, bar

Z F

acto

r

SRK @5C

SRK @10C

SRK @15C

AGA-8 @5C

AGA-8 @10C

AGA-8 @15C

UiO MEK4450 17

November 2013

Reservoir Fluids

0

20

40

60

80

100

120

140

160

-200 -100 0 100 200 300 400 500

Temperature, oC

Pre

ssu

re, b

ar

Gas Cap

Oil

20vol% Gas

40vol% Gas

60vol% Gas

80vol% Gas

Bubble Point

Bubble Point

Dew Point

Dew Point

99.99vol% Gas

99.9vol% Gas

99vol% Gas

UiO MEK4450 18

November 2013

Process Threats


19

Threat Device Mitigation

Sand Pumps/valves Separators and strainers

Droplets (Carry-over) Compressors Scrubbers and internals

Slugging Pumps/compressors Inlet Separator Volume

Deposits All Chemical Treatment

Subsea Transient Effects


20

Device Normal Condition Transient Condition

Pump Liquid filled Gas-filled

Gas slugs

Sand-free Sand «slugs»

Discharge flow Blocked discharge

Compressor Gas-filled Liquid-filled

Liquid slugs

Carry-over

Sand-free Fines

Electric Driver Clean dielectric Gas-contaminated

Sour

Water contaminated

Fines

Bearings Clean Lubricant or Gas Sand

Liquids

Facility Complexity


21

Suppliers

Compressor: GE

Switchgear: GE

Variable Speed Drive: GE

UPS: GE

Connectors: Tronic/Deutsch

Scrubber: Aker

Pump: Aker

Recycle Cooler: Aker

Compressor

UiO MEK4450 22

November 2013

Building the model: Goliat


23 Based on net available data

Reservoir Fluids

0

20

40

60

80

100

120

140

160

-200 -100 0 100 200 300 400 500

Temperature, oC

Pre

ssu

re, b

ar

Gas Cap

Oil

20vol% Gas

40vol% Gas

60vol% Gas

80vol% Gas

Bubble Point

Bubble Point

Dew Point

Dew Point

99.99vol% Gas

99.9vol% Gas

99vol% Gas

UiO MEK4450 24

November 2013

Gas-Lift System Overview


25

Compressor Station

Gas in Annulus

Mandrels

Control Valve

Artificial Lift Options


26

Water-Filled

Co

mp

ress

or/

Pu

mp

Oil-Filled Two-Phase

Co

mp

ress

or/

Pu

mp

Co

mp

ress

or

Liq

uid

Aft

er

Op

era

tio

n o

r fr

om

Ho

ldu

p

Liq

uid

Ho

ldu

p p

lus

Co

nd

en

sati

on

Condensation

Gas Lift

Example Case


27

Gas-Lift Point at 1050 m TVD (seabed) Two Tubing Sizes (3.5” and 5.125”) Initial GOR = 110 Sm3/Sm3

PI=250 Sm3/bar/day (all phases) 25% water-cut Simple fluid model (fixed phase split)

Approach


28

1. Start-up dynamics • Oil-Filled • Water-Filled

2. Operating Case • 3.5 and 5.125” tubing

Depth02550751001251501752002252502753003253503754004254504755005255505756006256506757007257507758008258508759009259509751000102510501075 Gaslift?11001125115011751200122512501275130013251350137514001425145014751500152515501575

Two-Phase

Gas-Lift Water / Mud Filled


29

Annulus Pressure 120 bar - Need Valve Cv at tree - Gaslift Valve Cv / Orifice - What else?

0

200

400

600

800

1000

1200

1400

0,0 50,0 100,0 150,0

De

pth

, m

Pressure, bar

Seawater

Gas

Oil Filled


30

Annulus Pressure 115 bar - Need Valve Cv at tree - Gaslift Valve Cv / Orifice - Is this Interesting?

0

200

400

600

800

1000

1200

1400

0,0 50,0 100,0 150,0D

ep

th,

m

Pressure, bar

OIl

Gas

In Operation


31

Annulus Pressure 105 bar + - Need Valve Cv at tree - Gaslift Valve Cv / Orifice - Annulus Pressure Drop

0

200

400

600

800

1000

1200

1400

0,0 50,0 100,0 150,0D

ep

th,

m

Pressure, bar

OIl

Gas

Operation


32

Depth02550751001251501752002252502753003253503754004254504755005255505756006256506757007257507758008258508759009259509751000102510501075 Gaslift?11001125115011751200122512501275130013251350137514001425145014751500152515501575

Two-Phase

Operation


33

How about the Compressor


34

T C 60 S1,ideal 136.5731 H1, ideal 10516.77 10516.77222 136.5731

1 2 3 4 5 6 P bar 35 Ss,ideal 136.8359 T2, ideal 149.8785 147.7694442 420.9194 136.5731

3 Z 0.954991 H2, Ideal 14082.59 13971.6931

Choke Sizing Calculator 4 mw 19.63837 dH, Ideal 3565.818 3454.920886 175.927

V1.2 5 v/f (volume) - 1.0000 H2, real 14974.04 dh, real 4318.651107 14835.42

6 P bar 110.1 T2, Real 184.58 164.157489

Inlet Pipe ID, in5.13 7 R kj/kmol/K 8.3145 H2, calc 15919.51 14835.42333 4318.651 219.9088

Choke Outlet Pipe ID, in5.13 8 Error -945.469 2.24052E-07

Choke Body ID, in5.13 9 polytropic adiabatic

Valve Style Modifier, Fd 1.00 10 Z 1.001245 0.727242 Z 0.994604

Liquid Pressure Recovery Factor, F11.00 11 efficiency η 0.8 efficiency η 0.8

12

13

14

15 v1/R v2,i/R

16 9.090152349 3.998329106

Tref , C 15.00 17 0.754729488 0.223460311 0.941596

Pref , bar 1.00 Feed 18 v1/R v2,i/R

Component mol% 19 9.090152349 4.16253813

Water 0.00 20 n 1.448968 1.384 k=Cp/Cv 1.32958 0.754729488 0.345024383 1.464132

H2S 0.00 21 1.464132 1.395373 -0.081

CO2 0.95 22 (n-1)/n 0.277 (k-1)/k 0.248

N2 8.85 23

Methane 78.96 24

Ethane 7.75 25

Propane 2.51 26

i-Butane 0.30

n-Butane 0.49

i-Pentane 0.08

n-Pentane 0.07 T C 184.58 T C 169.45

Benzene 0.00

Toluene 0.00

e-Benzene 0.00

o-Xylene 0.00

m-Xylene 0.00 Density

p-Xylene 0.00 mw kg/m3

Hexane 0.02 84.40 670 head kj/kg 181.7094 head kj/kg 178.5325

Heptane 0.01 92.60 734

Octane 0.00 105.20 760

Nonane 0.00 117.70 781

Decane 0.00 171.50 800

Total Head kj/kg 227.1367 Total Head kj/kg 223.1657

pk

k

n

n

h

111

gasideal

1

1

2

1

2k

k

P

P

T

T

gasreal

1

1

2

1

2n

n

P

P

T

T

11

1

1

211n

n

pP

P

MW

RTZ

n

nH

11

1

1

211k

k

aP

P

MW

RTZ

k

kH

11

1

1

1

211n

n

p

totalP

P

MW

RTZ

n

nH

h

2

1

1

2

ln

ln

P

P

n

i

P

P

k

,2

1

1

2

ln

ln

Note: 1st Iteration Result

Schultz Approximation?


35

Bubbles: Compressors and Pumps WIP

v2013 Gas

Gas Rate Oil Rate MEG Aqueous Rate Inlet T Inlet P Discharge PDischarge T Gas RateCompressibilityGas DensityGas Mol Wt Gas Cp/Cv Enthalpy

Sm3/d Sm3/d wt% Sm3/d oC bar baroC m3/d Z Tf c,Pf c Tf c,Pf c Tf c,Pf c Change

1 1000.0 0.00 0.00 0.00 60.00 35.00 41.22 72.948 31.5 0.95 26.11 19.64 1.33 25.36408

2 1000.0 0.00 0.00 0.00 72.95 41.22 48.55 86.141 27.8 0.96 29.55 19.64 1.33 26.212

Inlet Pipe ID, in5.13 3 1000.0 0.00 0.00 0.00 86.14 48.55 57.18 99.565 24.6 0.96 33.45 19.64 1.33 27.07727

Choke Outlet Pipe ID, in5.13 4 1000.0 0.00 0.00 0.00 99.57 57.18 67.34 113.210 21.7 0.96 37.85 19.64 1.33 27.96542

Choke Body ID, in5.13 5 1000.0 0.00 0.00 0.00 113.21 67.34 79.31 127.063 19.2 0.97 42.81 19.64 1.32 28.88544

Valve Style Modifier, Fd 1.00 6 1000.0 0.00 0.00 0.00 127.06 79.31 93.40 141.110 17.0 0.97 48.40 19.64 1.32 29.85079

Liquid Pressure Recovery Factor, F11.00 7 1000.0 0.00 0.00 0.00 141.11 93.40 110.01 155.342 15.0 0.98 54.67 19.64 1.32 30.88048

196.2355

Tref , C 15.00

Pref , bar 1.00 Feed

Component mol%

Water 0.00

H2S 0.00

CO2 0.95

N2 8.85

Methane 78.96

Ethane 7.75

Propane 2.51

i-Butane 0.30

n-Butane 0.49

i-Pentane 0.08

n-Pentane 0.07

Benzene 0.00

Toluene 0.00

e-Benzene 0.00

o-Xylene 0.00

m-Xylene 0.00 Density

p-Xylene 0.00 mw kg/m3

Hexane 0.02 84.40 670

Heptane 0.01 92.60 734

Octane 0.00 105.20 760

Nonane 0.00 117.70 781

Decane 0.00 171.50 800

PhasePhase

Solution Strategy


36

Optimum: Really?


37

The ESP Overview


38

Speed Controller

Cable

Motor Pump

ESP Performance


39

Rotating EQPT = Vendor Sizing

But We Can Estimate


40

Need to consider Operating Points

Seabed Booster System Level


41

Power • Variable Speed Drive • Switch Gear • Transformers Process • Slug-catcher • Mixers • Recycle Coolers • Barrier Fluid • Lubricants

Seabed booster


42

Barrier Fluid and Lubricants


43

Problem: Protecting the motor and bearings Solution: Applying a pressurized fluid Helps Control Bearings

Mo

tor

Pu

mp

Ba

rrie

r F

luid

Flo

w

Compressors and Pumps: Bearings


44

How to provide a stiff support for a shaft

1- Support it in a liquid lubricant 2- Support it by magnetism 3- Use rollers

Bearings


45

Journal bearing: 1. Simplest and stiffest 2. Lubricant functions as coolant

Magnetic 1. Complex control

Film

Lubrication Models


46

Film

Flow Laminar Heat transfer Simple

Finally: Compressor Maps


47

Rate

He

ad

UiO MEK4450 48 November 2013

Enthalpy-Entropy Diagram

-1.0E+05

0.0E+00

1.0E+05

2.0E+05

3.0E+05

4.0E+05

5.0E+05

6.0E+05

-2000 -1000 0 1000 2000

Entropy, J/kg/C

En

tha

lpy

, J

/kg

5oC

25oC

65oC

125oC

165oC

185oC

1 bar 26 bar

6 bar

36 bar

16 bar

135oC

155oC

175oC

195oC

215oC

115oC

95oC

75oC

55oC

35oC

15oC 45oC

85oC

145oC

105oC

205oC

225oC

11 bar

21 bar

31 bar

41 bar

UiO MEK4450 49

November 2013

Reference Fluids

DEMO2000 Application

Luciano E. Patruno

November 2011

Treated use entropy-enthalpy balance.

Pressure-Enthalpy Diagram for Water and Steam Based on the IAPWS-97 Formulation for General and Scientific Use

0.01

0.1

1

10

100

1000

0 500 1000 1500 2000 2500 3000 3500 4000

Enthalpy, kJ/kg

Pre

ssu

re,

ba

r

Copyright © 1998 ChemicaLogic Corporation. Drawn with SteamTab Duo V3.0.

Hi

deal hideal/

h

UiO MEK4450 50

November 2013

Documents

Subsea Boosting Day 2 November 2014 Jørgen Wessel thermodynamic design and test evaluation of centrifugal compressors is frequently based upon a polytropic analysis employing perfect-gas